Introduction

The semantics and pragmatics of questions have long been the object of linguistic
exploration, as usefully reviewed by Judith Blanchette (Questions
in the Online Learning Environment, 2003) and by Michiel Borkent and
Riemer van Rozen (On
logic and questions in dialogue systems, 2004). Several types of questions
in English are distinguished: yes/no questions, WH-questions, alternative questions,
tag questions, and intonation questions.

There is an extensive literature on those referred to as "WH-questions"
(see Robert D. Van Valin, Jr. The
Acquisition of WH-Questions and the Mechanisms of Language Acquisition).
These are notably considered of importance in language teaching. The set consists
of questions such as: Who, Why, Where, What, How, When, Whether, Whither, Whence.
All these forms are ultimately derived from an Indo-European root (kwo-),
a stem of relative and interrogative pronouns. In Latin and Romance, the corresponding
forms generally begin in "qu-" (e.g.Latin quid, quod;
French qui, quoi, quand, etc).

Semantic interrelationships between WH-questions

The semantic relationships between WH-questions do not appear to have been
explored, the main focus being on pragmatics, intonation, and comparative syntactical
issues across languages. For example, Lisa Lai Shen Cheng (On
the Typology of WH-Questions. 1991, 1997) proposes that the typological
distinctions among languages with respect to the formation of WH-questions can
be attributed to the availability of question particles and the properties of
WH-words. Unfortunately, the problem of identifying question type has long been
recognized as a difficult one.

Michiel Borkent and Riemer van Rozen (On
logic and questions in dialogue systems, 2004) move towards such an
exploration through logical relationships in a "logic of questions"
(analogous to a logic of propositions). Their interest is in how a logic of
questions can contribute to the analysis of questions in dialogue systems and
their improvement -- in order to "lift the work in this field to a higher
level".

Hui Yang, et al. (Modeling
Web Knowledge for Answering Event-based Questions, 2003), in discussing
the correspondence of WH-questions and event elements, conclude that a QA event
shows great cohesive affinity to all its elements and the elements are likely
to be closely coupled by this event:

Who/Whose/Whom: Subject, Object

Where: Location

When: Time

What: Subject, Object, Description, Action

Which: Subject, Object,

How: Quantity, Description

But it might also be asked whether there are other kinds of WH-questions characteristic
of other epistemological mindscapes in the light of the arguments of Magoroh
Maruyama and others (see Systems
of Categories Distinguishing Cultural Biases, 1993). Irrespective of
the syntactic structure and the use of intonation in questioning, which are
a major focus of linguistic research, there seems to be an interesting assumption
that the set of WH-questions (however constructed) is semantically invariant
across languages -- perhaps as a feature of a universal grammar. This would
be curious given the recognition of the existence of languages with minimal
distinction of numbers and colours -- and richer distinctions with regard to
features characteristic of their environment (eg snow, etc).

Although interrelationships between them do not however appear to have been
directly addressed, the Principia
Cybernetica integrates them -- in relation to eternal
philosophical questions -- into the articulation of a complete world view.
It is also instructive to reflect on the ways in which the dynamics of the "Garden
of Eden" -- as an archetypal epistemological space -- can be framed in
terms of the complementarity amongst such "WH-questions".

Given their fundamental role, as a semantic or cognitive set, the concern here
is the possibility that the WH-questions may be interrelated in a particularly
interesting way. This is seen to be of relevance to:

strategic decision-making for individuals or groups and the questions appropriate
to critical thinking and the vigilant avoidance of dysfunctional groupthink

self-reflexiveness in navigating reality (especially the experiential dimensions),
whether understood as philosophy (elucidation of alternative epistemological
frameworks) or as engagement in an alternative lifestyle

engagement on any (vision) quest (especially given the relationship of "quest"
to "question")

The relationships between the WH-questions might usefully be understood as
a form of cognitive knot -- different threads weaving to form a cognitive fabric
(a "magic carpet"). The threads involve a degree of entrainment /
entailment / enaction / engagement with reality. Each is associated with a different
kind of dynamic connection or framing: the "why energy", the "who
energy", the "where energy", the "what energy", the
"how energy", etc. However it is highly probable that the terms (or
their syntactic equivalents) are used in discourse in ways that blur recognition
of the unique functions to which they relate. Some terms using one form may
in fact reduce to another: "How long before it rains?" may
be reduced to "When will it rain?" The terms may therefore
be rough pointers to a semantic or cognitive set which is the focus of what
follows.

Engaging with tendencies to twisting movement -- insights
from helicopter control

An interesting approach to the nature of the integration performed by any practitioner
of movement is offered by the work of Arthur
Young in Geometry
of Meaning(1978). His insights derived from his engagement
in the development of the Bell helicopter. His learnings developed from reflection
on how such a vehicle could be navigated in three dimensions in a controlled
manner -- responding to the challenging tendencies for the vehicle to twist
out of control in various ways. This could be seen as the basis for a useful
articulation of the challenge for any body to navigate in a complex space. Such
knowledge is the basis for successfully undertaking challenging sports involving
a high order of kinetic intelligence.

In Young's original presentation, the vehicle was a helicopter.
In the more general case it could well also be applied to the human "vehicle"
in the Buddhist sense -- or any conceptual vehicle. In marked contrast with
the classic static presentations of virtues and vices in any culture, his approach
introduces the dimension of time that is central to movement in different ways.
It emphasizes the way in which movement is coordinated -- and how attributes
such as "momentum" are used in complex manoeuvers by practitioners.
From such a perspective, an attribute like "inertia" may be of considerable
positive significance -- in contrast with its negative characterization as vice
(cf in Christianity) or fetter (cf in Buddhism) of "sloth".

As briefly expressed elsewhere (see Navigating
Alternative Conceptual Realities: clues to the dynamics of enacting new paradigms
through movement, 2002), there is a lack of operational specificity
to the various static "guidelines" to movement in semantic space. But as those
participating in many sports would probably argue, it takes experience to learn
what subtle experiential meaning is associated with attitudes appropriate to
any "code words" about improved performance. Much may be achieved with inappropriate
attitudes, but they do not raise the level of performance beyond a certain degree.
Ultimately the person is judged as lacking something subtly associated with
"style", "élan" and "flow". Basically the performance
is not sustainable. In this respect the relationship, in Buddhist meditation
practice, between the "hindrances" and "fetters" encountered, and the articulation
of necessary values, is somewhat more explicit.

Measure formulae as the basis for a semantic template

WH-questions (Where, Why, When, How, etc) are basic to piloting a vehicle.
A pilot must constantly ask and answer such questions, whether consciously or
unconsciously. What is required is a fundamental way of interrelating the WH-questions
and determining how they are necessary in order to navigate other spaces --
including that of experiential reality. A valuable lead in this is the work
of Arthur Young (The Geometry of Meaning, 1978) on measure formulae and the
learning/action cycle (despite the reservations of Frank Barr: Toward
a Solution of the "Big Questions", 1988). His work is particularly valuable
because of the mindset he had to cultivate in developing the Bell helicopter
-- a fundamental challenge to controlled movement.

For Young, in discussing the "categories of knowing represented by measure
formulae", he argues (pp 20-21):

What are these measure formulae, position, and its derivatives, velocity
and acceleration? Are they just the simple "physical quantities"
as they are referred to in textbooks?

Not so. closer examination reveals fundamental qualitative differences
between them...Position can only be observed visually or by less direct
processes. Velocity is an intellectual abstraction: it cannot be known from
direct experience. It must be computed. To known velocity, we must make two
observations of position, determine their differences, and divide the time
elapsed, thus obtaining a ratio... Acceleration, however, is felt.
For example, when an elevator suddenly starts down, you feel it....
[emphasis in the original]

Young continues in a discussion of "generating other measure formulae"
(pp 32-33 ):

In the pursuit of meaning, the measure formulae are invaluable because they
replace words...The measure formalae, as we have seen in the case of length
(L) and its derivatives, are more explicit than words in that they define
operations, like the operation of the derivative. Thus they anticipate the
aspects or categories that we may expect a situation to have....The measure
formulae are the outcome of centruies of struggle on the part of physical
science to arrive at a set of terms than can be formulated in such a ways
as to leave no vagueness, no ambiguity. They describe the skeletal anatomy
of all science, and even anticipate modern discoveries...

The measure formulae we have considered -- position and its derivatives --
are given in terms of two variables, length (L) and time (T). These two variables,
more correctly referred to as parameters, together with a third, mass (M),
are the basic ingredients of physics, more basic than the formulae, as they
are fewer in number; the formulae are combinations of these parameters...[as]..
the "undefined terms," the fundamental ingredients from which all
measure formulae are constructed.

Young then demonstrates the generation of other measure formulae (see Table),
noting that of the twelve, 10 (recognized by physics) are used to analyze the
dynamics of a moving body, whilst 2 are "not presently recognized in physics
textbooks, but used in engineering".

Generation of Measure Formulae
(according to Arthur
Young)

Group I

Group II

Group III

L= position

x M =

ML= moment

x L =

ML2 = moment of inertia

L/T = velocity

ML/T = momentum

ML2/T = action (rate of change
of inertia)

L/T2 = acceleration

ML/T2 = force

ML2/T2 = work

L/T3 = control

ML/T3 = mass control

ML2/T3 = power

Qualitative operational relationships associated with learning
cycle

In seeking to use this as a possible template for recognizing the semantic
relationships amongst the WH-questions, the point to be made is that such questions
are, to an important degree, focused on orientation and movement in semantic
space-time, whereas the Young framework builds on the challenge of moving
in physical space-time. The WH-questions may thus be understood as different
kinds of informational interaction with the semantic context that are necessary
for controlled movement in that context. Of particular significance, in the
interaction through such questions, is the process of learning through which
questions are refined -- hence their current relevance to information retrieval
system design.

Young himself focuses at length on the nature of the learning cycle in elaborating
what he terms a "Rosetta Stone" of meaning. This is "not just
a translation of meaning, but is a generation of meaning. It is the relationships
between the words we must use, not their definitions, that give them their meaning"
(p. 38). With respect to the learning cycle, he distinguishes four basic categories
of act, relationship and state that he interrelates as
follows:

Basis of Rosetta Stone of Meaning
(according to Arthur
Young)

Relationship

Act

State

impulse (purpose)

spontaneous act

being

faith

change (reaction)

transformation

knowledge (form)

observation

significance

fact

control

establishment

He addresses the challenge of relating this learning cycle to the set of measure
formulae on the following basis:

We shall use the cross axis as a format for analysis to bring out the meaning
implicit in the angular relationship between the terms. Recall that factors
at opposite ends of an axis are mutually opposed, that those at right angles
to one another are independent, and that rotation signifies change in time.
(p. 41)

Cognitive instruction set for a semantic vehicle

The table below uses a clumsy array of approximate terms to identify a possible
set of complementary ways for the "driver" of an existential "all-terrain
vehicle" to "handle" the relationship with the environment. Each
mode suggests a different way of using energy to act coherently, although all
are necessary according to the nature of the challenge. The presentation is
distorted because it underemphasizes the ways in which the challenge from the
environment may invite a gentler and more seductive response than is suggested
by the metaphor of driving an all-terrain vehicle -- a metaphoric trap with
which the world is now all too familiar.

Significance[Where/Why]
Provenance: Where does that come from? Why is it significant?

Knowledge[Where/Who]
Where is the knowledge?
Who has it? Who discovered it?

Which?(Which way? Which to choose?)

Change[Which/How]
Which response? How to respond?

Transformation[Which/Why]
Which transformation and why?

Faith[Which/Who]
Which belief? Who to believe in? Who believes?

When? (When to start? When to stop?)

Spontaneous
act[When/How]
When to act? How to act?

Being[When/Why]
When to be like that? Why be like that?

Impulse[When/Who]
When to start? Who is so impelled? Who to impell?

What?(What is it? What to do?)

Control[What/How]
What do I do? How do I do it?

Establishment[What/Why]
What have I done? Why have I done it?

Fact[What/Who]
What evidence is this? Who says so?

Challenge of interpretation and comprehension

The preceding tables pose fundamental challenges to comprehension which are
addressed by Arthur Young's more detailed arguments regarding their two-fold,
three-fold and four-fold dimensionality. The basic challenge is the distinction
between:

comprehending and embodying the relationship between the varieties of experience
so categorized

This is the distinction between memorizing a detailed manual on flying a helicopter
and the actual ability to coordinate the different cognitive operations essential
to that process. This might be understood in terms of the term "operacy"
as promoted by Edward de Bono:

In education we are concerned with literacy and numeracy. That leaves out
the most important aspect of all, which I call "operacy". The skills of action
are every bit as important as the skills of knowing. We neglect them completely
and turn out students who have little to contribute to society. [more]

In exploring the above tables, the challenge is to avoid being locked into
a particular style of question in relating to any context, whether:

by cell: how/when, or who/what, etc

by column: how, why, or who

by row: where, when, which, what

This applies in particular to use of the same style of questioning in exploring
the above pattern of questions! The perspective called for (in piloting a "cognitive
helicopter") is the ability to shift appropriately between the question
-- a detachment from any one of them as a preference (like preferring 2nd gear
in an automobile). Piloting is the ability to shift appropriately. [black helicopters]

One way to characterize the trap is to compare the form of the table to the
frontal view of many multi-storied buildings. The eye moves most readily over
the alienating rectangular patterns of that form. This has very little to do
with any cognitive dimensions which are portrayed and interrelated through that
form. This is best recalled by recognizing the fundamental nature of questioning
and the dynamic application of questions in areas such as:

philosophy: who am I, etc

evidence in science: what is it, how does it work

evidence in crime: how, why, who, etc in relation to identification of means,
motive and opportunity with regard to suspects

choice as a consumer: the complex process of determining needs, and selecting
products to meet those needs, on a daily basis

acquiring information: especially through web retrieval systems using search
engines, and the associated learning processes through which searches are
refined

relationships: will s/he, won't s/he?

self-development: integrating and embodying insights emerging from a succession
of action learning cycles and reflection on life experience (as exemplified
by the statement "an unexamined life is not worth living")

narrative coherence: understood as an interwoven pattern of basic questions
and answers (interlocking cycles of action and learning) that derives its
interest from a transformation and reframing of perspective

Another aspect of the trap is evident in the case of proprietary systems of
categories by which questions and answers are configured. The current market-oriented
approach to exploitation of knowledge and insight results in many such frameworks
being copyrighted, or restricted to use under license. An example is the Myer-Briggs
Type Indicator® (MBTI® ) a registered trademark of Consulting
Psychologists Press, Inc., the publisher of the MBTI instrument. What can
be copyrighted does not hold the dimension essential to new understanding --
but could essential questions or answers be coyprighted?

The quality denoted by the label associated with the cell of a table above
is a dynamic resolution of two questions. The label points to a dynamic answer,
holding (or embodying) the unresolved (unanswered) dimensions of the question
constituted by a strategic dilemma in piloting the cognitive vehicle. The quality
associated with the cell does not bring closure to the questions associated
with it. The "focus" is "in" rather than "on"
the dynamic -- it is not a static focus.

Answers to why where who what how questions are of a form different from
the yes-no form.

Questions are posed to gain knowledge.

Questions exist in dialogues, and must be spoken out loud.

The emphasis in many such conventional approaches to the study of questions
and answers ("Q&A") is in the direct connection between question
and answer. Specific questions imply specific answers. A question that cannot
be answered is not a proper question. Answers are designed for specific questions
(FAQs).

Such a Q&A framework does not respond to many subtler existential questions
that emerge in navigating the cycles of daily life -- for which "satisfactory"
answers may be sought in distraction (entertainment, substance abuse, etc),
consumerism, religion or sex. This recalls the adage: "For every complex
problem, there is a solution that is simple, neat, and wrong". Some questions
do not go away -- because the answers available are not satisfactory. This is
most obvious for many young people in the case of what to do with one's life.
It is evident to all in relationships -- where the response to a key question
may be "maybe".

The existential nature of the quandry is well-illustrated by the function of
a koan posed to a student by a Zen master. The koan is indeed a "question"
which can be asked: "What is the sound of one hand clapping"? There
are many possible "answers", which although credible are "wrong".
The essential role of the koan is to evoke a different attitude that effectively
reframes the question and any possible answer. The answer is in the transformation
of perspective -- a learning that is quite distinct from what is conventionally
understood by the retrieval of information (as with a riddle).

The contrast can perhaps be most briefly described as between an immediately
comprehensible answer and one that requires learning. What we need to understand
may only be expressible in a language we do not know.

Elsewhere de Bono has explored the use of sets of cognitive "hats"
and "shoes" (Six Thinking Hats, 1987 and Six Action Shoes,
1991). The "shoes" are notably in relation to his understanding of
operacy -- which would be a key to the operation of any cognitive helicopter.
As he puts it: "Most executives, many scientists, and almost all business school
graduates believe that if you analyze data, this will give you new ideas. Unfortunately,
this belief is totally wrong. The mind can only see what it is prepared to see."

The "pathology" of a mono-modal thinking approach might be understood
in terms of so-called "freaks":

Control freaks

Faith freaks (fundamentalists)

Observation freaks (trainspotters, "twitchers")

Action freaks ("action man")

Being freaks ("hanging out")

Establishment freaks (status)

Change freaks

Transformation freaks (self-improvment)

Significance freaks

Knowledge freaks

Fact freaks ("trivial pursuit")

Existential dynamic in a "cognitive helicopter"

As noted earlier, the challenge of piloting a helicopter was the inspiration
for Arthur Young's model -- used here to order WH-questions relating to movement
in semantic space. Such are the cognitive challenges of helicopter movement
that a study has in fact been made of a "cognitive helicopter" (A.
Walsdorf, et al. Cognitive Helicopter Cockpit: From Human Operator to a Cooperation
between Man and Cognitive Assistant System, Internationales Hubschrauber
Forum 2000, Bückeburg). Of course the focus there is on the "helicopter",
whereas here the concern is with "cognition".

WH-interactions with "reality", and how the latter is reframed and
re-engaged by that process, might be understood as what being alive is all about.
WH-interactions are what is happening moment by moment to sustain relationship
with reality and be nourished by it. Those interactions are like a cognitive
form of REM (rapid eye movement).

It would be very interesting to explore WH-interactions from a perspective
of different kinds of meditation -- especially those so highly articulated by
Buddhism. Meditation might indeed be understood as piloting a cognitive helicopter
-- as "cognitive helicoptering". The higher disciplines of meditation
purportedly involve engaging with reality so as to reframe the knower-known
relationship. Who asks the questions? Who answers?

Ironically the term "helicopter" derives from the Greek adjective
"elikoeioas," (Latin "helix")meaning spiral or winding
and the noun "pteron," meaning feather or wing.

The ability of a helicopter to rise vertically and move in any direction is
consistent with the freedom sought in many forms of meditation. Both "helix"
and "wing" are significant metaphors in meditation. Again, the capacity
to "hover" in place might be compared with the quality of detachment
from mundanities -- as sought in meditation -- or the appropriate navigation
of patterns of virtues and vices (Navigating
Alternative Conceptual Realities: clues to the dynamics of enacting new paradigms
through movement, 2002). Insights of relevance are also articulated
in relation to aerobatics (see Why
Hummingbird?, 2002). Arthur Young in 1946 moved on from his work on
the helicopter to an interest in the psychopter -- the helicopter as a metaphor:
"What is the Psychopter? It is the winged self. It is that which the helicopter
usurped -- and what the helicopter was finally revealed not to be." (The
Bell Notes: A Journey from Physics to Metaphysics, 1979). It might even
be instructive to consider the parallels between the earliest efforts at helicopter
design [more]
and exploration of the psychological technologies of meditation.

In the case of a helicopter, and in accordance with Newton's law of action
and reaction, the helicopter fuselage tends to rotate in the direction opposite
to the rotor blades. This effect is called torque. It is associated with the
geometric center of the main rotor and results from the rotor being driven by
the engine power output. It must be counteracted and or controlled before flight
is possible and must be continually corrected during any manoeuvers:

Compensation for torque in the single main rotor helicopter is accomplished
by means of a variable pitch antitorque rotor (tail rotor) located on the
end of a tail boom extension at the rear of the fuselage. Driven by the main
rotor at a constant ratio, the tail rotor produces thrust in a horizontal
plane opposite to torque reaction developed by the main rotor. Since torque
effect varies during flight when power changes are made, it is necessary to
vary the thrust of the tail rotor. [more]

A form of "torque" has been considered of significance in relation
to schizophrenia (T Blau. Torque and schizophrenic vulnerability: as the world
turns. American Psychologist, 1977, 32, 997-l005). the question of "psychic
torque" seems to have been explored by Eddie Oshins whose lifetime interest
in martial and meditative arts was reflected in an experimental proposal for
measuring certain forms of self-referential motion predicted by his theories.
Through his Quantum
Psychology project, he proposed a modification of the results of experiments
with monkeys by A. P. Georgopoulos, which indicate neuro-correlates for mental
rotations such as have been shown to occur in mental imagery by R. N. Shepard
and colleagues. Oshins suggested a simple experimental adaptation from the wing
chun kuen martial art's "siu nium tao form" to derive data supporting
his hypothesis of a "psychic torque." [more]

Non attachment is integral to Zen and if we foster it in our relationships
with others we free ourselves, and others, from the emotional torque that
all too often leaves us spiraling out of control. If we abide in the path
of non-attachment, we won't get pulled into the tormented existence of the
drug-abuser or the thief, and we'll be able to provide unbiased, selflessly
motivated guidance when troubled people come to us for help.

Modern individuals want to drive actively, which can also mean fast, but
not irresponsibly and always with the sense of having the vehicle completely
under control. They want to enjoy a "sports-oriented" driving experience
and feel the power in their vehicle.

Challenge of closure

Implicit in a focus on questions is a search for "closure". An answer
provides a degree of closure -- effectively de-energizing or discharging the
question. Paradoxically the "closure" provided by an answer may be
in some cases characterized by an unusual form of "openness" -- acknowledged
notably through the insights triggered in answering a koan. Curiously the "challenge
of closure" is also of particular importance to Christian evangelism:

As the century draws to a close, mission leaders are increasingly talking
about the subject of "closure". Here, then, is a working definition. Closure:
The completion of the task of presenting the Gospel to every person in the
world -- in his mother tongue, or an understandable trade language -- while
providing an opportunity for those who respond to grow toward maturity in
Christ through a local body of believers. [more]

The challenge of closure has been extensively explored by Hilary Lawson (Closure:
A Story of Everything, 2001). It is an attempt to provide an account that
overcomes the problems of self-reference inherent in other philosophical systems.
In the words of one reviewer, Tim Gwinn (2004):

Both realism and relativism take as a basis that there is some 'thing' -
namely, the world - to which these accounts are deemed to apply. By contrast,
the beginning in Closure is to not take the world as a 'thing' to be
grasped or understood. Instead, the world is to be thought of as the "openness",
which is the site or space of possibilities that occur in the absence of our
attempts at comprehension. Lawson uses the phrase "undifferentiated flux"
as another way of attempting to illustrate the notion of "openness". (But
this is illustrative and not meant to indicate some physical "flux".) In this
sense, "openness" is not a 'thing', but a lack of our imposing of closures.

"In the context of the individual, openness can be conceived as the other
of experience. Not as a collection of things that are the external cause
of inner experience, but as the space within which experience takes place.
In addition, openness can be conceived as the other of language. Once again,
not as that to which language apparently refers, but as the space within
which the activity of language takes place." [p. 3-4]

'Things' occur with closure. "Closure can be understood as the imposition
of fixity on openness....It is the conversion of flux into identity, the conversion
of possibility into the particular." [p. 4] [more]

The inadequacy of any explanatory closure is also the fundamental theme of
Kurt Gödel's incompleteness theorem (1931) with regard to mathematical
and philosophical questions -- proven by a particular use of prime number theory
(see E Nagel and J R Newman. Gödel's Proof, 1958) [more].
This challenge has also been explored by Douglas R. Hofstadter (Gödel,
Escher, Bach: an Eternal Golden Braid, 1979)

Self-reflexively, in relation to the more appropriate exploration of more insightful
questions that is the theme of this paper, it may therefore be asked what
kind of closure is sought by who -- when, where and how
-- and why?!

Reframing possibilities of closure

Rather than seeking the stasis normally associated with closure, the emphasis
here is on the nature of the dynamics associated with navigation in the knowledge
space through continual interactive questioning of that context.

This might be understood as the cognitive analogue to the challenge of Arthur
Young in developing the helicopter. This is likely to have been what led to
his later exploration of process thinking. Young's Theory
of Process is a formal analytical tool, a model based on number theory,
geometry and topology -- as well as on traditional wisdom disciplines and other
modes of knowledge and insight -- in an effort to help comprehend and integrate
a number of disciplines and areas of inquiry. One articulation in physical terms
of this challenge is the thesis summary of Shumin Zhai (Human
Performance in Six Degree of Freedom Input Control):

This thesis is concerned with design factors that influence human performance
in manipulating the location and orientation of three dimensional (3D) objects
with six degrees of freedom (6 DOF). The need for this research has emerged
from the development of a variety of advanced technologies. Technologies such
as virtual and augmented reality (Barfield and Furness, 1995) telerobotics
(Sheridan, 1992b), computer aided design (Majchrzak, Chang, Barfield, Eberts,
and Salvendy, 1987), scientific data visualisation (Card, Robertson, and Mackinlay,
1991), and 3D computer graphics and animation (Foley, van Dam, Feiner, and
Hughes, 1990) all require designing interfaces to let human users control
6 degrees of freedom of objects (robot, data, or viewpoint) in 3D space.

Given the many and varied approaches touching on the cognitive challenge, it
would also be totally presumptuous to seek closure. In fact it is more interesting
to see the many approaches as interweaing -- twisted together in various kinds
of knot -- into a pattern whose outlines preclude closure, even when they can
be intuitively recognized to some degree. Perhaps as some form of cognitive
Klein bottle?

Some of the tantalizing approaches that enrich this understanding are presented
in the following table. It would be good to think that the dimensions of such
a table could point to a higher ordering of the preoccupations that it endeavours
paradoxically to hold. Could they be usefully ordered in terms of WH-questions
with respect to higher order reality?

Approaches: clues to ways of engaging with higher
order reality

Each maps into the other through complex transforms
of which they are each respectively a metaphor

Each is itself a knot and its own metaphor (symbol,
configuration, question, etc)

Helicoidal coding

The processes by which any one such approach maps into another call for particular
attention. For example, Xavier Sallantin has long taken a very fundamental approach
to the natural foundations of digital data processing aimed at the exegesis
of machine languages (Le
Métalangage naturel de l'informatique digitale). This raises questions
about the relationship to Young's approach. In Sallantin's application of the
theory (Genetics:
the digital key to genetic coding, 2001) he postulates and exploits
an ontological connection between the elementary logical functions and the physical
functionings.

In theory these functions are defined by conjugating three arithmetical idealities: the ideas of zero, unity and duality. The phenomenal expression of this
conjugation is allowed by the fundamental variables Time, Force and Space,
as well as being conjugated within any action. These first correlations among
arithmetical signified and physical signifiers enable one to write the formula
of three basic semantemes, or so called metasemes, the constituents of the
meta-language of digital data processing. These three original metasemes are
natural radicals of meaning, necessary and sufficient for the elaboration
of all machine languages implemented by computers. The purpose of this paper
is not to present the theory of univocal arithmetic but its application to
genetics. Because of this, the study limits itself to the least one needs
to know about these three original metasemes in order to give evidence that
a fourth arithmetical ideality, the idea of three, is in fact implied by these
three correlations.

In relating this approach to the fundamentals of genetics, he notes:

It is a well known fact that the genetic message is written with words of
three letters, codons, taken from an alphabet of four letters, puric bases
(in short U, C, A, G). The starting hypothesis retained is that this message
is a coded message; in other words these four bases are the natural writing
ciphers, namely the four representational figures of the numbers 0, 1, 2,
3 of the quaternary numeration system. In fact, if one writes these four figures
by means of the four doublets of binary numeration: Zéro=00, One=01,Two=10,
Three=11, then the codons become sextuplets consisting of the only two figures
or digits, 0 and 1, used by the binary notation system. The 64 codons are
therefore the first 64 integers, from 0 to 63.

In discussing the natural digitization of codons, Sallantin notes:

More precisely, unlike the animal, the sapiens is capable of performing mathematics
and poetry because he can find a way inside the fractal piling of abstraction
and symbolization levels. He has a compass allowing him to distinguish between
the inductive ascent and the deductive descent....Whereas the left-hemisphere
is specialized in the reductive descent towards increasing abstraction, the
left-hemisphere is specialized in the creative ascent towards increasing symbolization
; in the same way as one is born left-handed or right-handed, some are more
endowed for objective reasoning and others for subjective imagination. Other
concomitant works of cerebral neurology demonstrate today this human privilege
of an innate programming that allows only the human newborn child to learn
the univocal numbering

But the fact that digitization is related to a reference system implies differentiating
between the level of the referred object and the the level of the referring
subject. Fractal dyslexia does not allow this differentiation for lack of
an agreement of neurons on a common standard. Only our faculty of reflection,
escaping this dyslexia, enables us to avoid confusing the inside representation
from the outside reality. T his faculty of reflection enables us to grasp
what has been lived from the outside so that it can be objectivized. In brief,
we can step out of a reality in order to seize its form which mathematics
will then translate by a formalism.

In other words, the identification number attributed on this plan by the
biologist working in classic univocal arithmetic to every codon could not
be the number used by Nature when it digitizes in the only ambiguous arithmetic
it uses. To discover this natural numbering, it is necessary to release oneself
from the human power of abstraction and to refrain from relating to a Cartesian
reference system....

Sallantin uses the details of experience on a helical pathway through a cube
of 64 numbered cells (extensively illustrated using a multistory parking lot)
to trigger this shift in perspective:

The helix threads being in opposite directions, these circuits are enantiomorphic
like our two hands. The Northern circuit goes through both upper floors of
the parking lot in double helix ; the Southern circuit goes through both lower
floors of the parking lot in double helix ; there is an inversion of the helix
thread of the Southern circuit when it changes floor, the same observation
applies to the Northern circuit.

Sallantin points to the possibility of a software simulation of this non-Cartesian
helicoidal trajectory "to feign the behavior of living people suffering
from fractal dyslexia and it will save effort here and relieve the individual
from the anthropomorphism of univocal arithmetic... NRA is indeed on the one
hand the corresponding interface between 64 codons, and on the other, 20 amino
acids and two punctuation marks".